kolmeenkolmeen

Kolmeenkolmeen is a fictional term used in discussions of combinatorial word constructions and puzzle design to describe a triadic recursive pattern. The concept is not part of formal linguistics or mathematics, but is employed in speculative or recreational contexts to illustrate self-similarity and symmetry in sequences.

Construction and notation: Start with a single symbol, S0 = A. For each level n+1, form Sn+1 by placing a new central symbol Cn+1 between three copies of Sn: Sn+1 = Sn Cn+1 Sn Cn+1 Sn. Each level uses a distinct central symbol, producing a triadic, self-similar structure. This rule emphasizes three-way repetition and recursive expansion.

Examples: S0 = A. S1 = ABABA. S2 = ABABACABABACABABA. In each step, a new center symbol is inserted and the previous level is replicated three times around it. The technique yields sequences with central symmetry around the inserted symbols and clear self-similarity across levels. A third-level sequence, S3, would be obtained by applying the same process with a new center symbol, resulting in a longer, 53-character string, but is typically not written out in full for brevity.

Characteristics and relation: Kolmeenkolmeen creates triadic recursion that mirrors itself at every level. It is related to other self-similar constructions like the ABACABA sequence but differs by enforcing three-fold repetition at each step. The pattern is mainly discussed in puzzle design and recreational mathematics as a way to study growth, symmetry, and recursive structure rather than as a standard formal concept.

Notes: The term is a niche neologism lacking formal standardization. It appears in online communities and speculative writing as a convenient label for this specific triadic recursive construction. See also: ABACABA sequence, self-similar sequences, recursive constructions.